By making numerical simulations the influence of resonant absorption in Er-doped fibres on the propagation characteristics of femtosecond pulses has been examined. It is shown that when the fibre background dispersion is relatively small compared to the dispersion caused by absorption, the pulses propagating in an unpumped Er-doped fibre can be either compressed or broadened, depending on whether the spectrum of the launched pulse is on the longer or shorter wavelength side of the absorption center. The phase distortion due to absorption has a more severe impact on the temporal profile of a propagating pulse than the corresponding amplitude attenuation. A switching of the sign of the actual fibre dispersion on one side of the absorption center occurs and this can lead to a change of pulse propagation characteristics from a soliton regime to a non-solitonic regime.